Question:

Find the number of 6-digit natural numbers where the digit sum is 10 and each of the digits 0,1,2,3 occurs at least once:

Step-by-Step Solution

Key Concept: Fixed digits: 0+1+2+3=6, remaining 2 digits sum to 4. Cases: (1,3), (2,2), (4,0). Count arrangements ensuring first digit $\neq 0$.

$\mathbf{490}$ numbers.

Correct Answer: 490